# Framework for Quantifying the Efficiency of Competing Signal Transmission Modes in Proteins

## TL;DR

This paper introduces a theoretical framework to quantify how efficiently different signal transmission modes work in proteins, using simulations and experiments.

## Contribution

A novel theoretical framework based on linear-response theory to analyze signal transmission modes in proteins.

## Key findings

- Signal propagation through coiled-coil motifs in histidine kinase occurs via shift, splay, and twist deformation modes.
- Splay deformation is the most relevant mode for the biological function of the histidine kinase protein.
- The framework was applied to analyze signal transmission in the β2-adrenergic receptor's structural domains.

## Abstract

On the microscopic
level, biological signal transmission relies
on coordinated transient structural changes in allosteric proteins
that involve sensor and effector modules. The time scales and microscopic
details of signal transmission in proteins are often unclear, despite
a plethora of structural information on signaling proteins. Based
on linear-response theory, we develop the theoretical framework to
define frequency-dependent force and displacement transmit functions
through proteins and, more generally, viscoelastic media. Transmit
functions quantify the fraction of a local time-dependent perturbation
at one site, be it a deformation, a force or a combination thereof,
that survives at a distant site. They are defined in terms of equilibrium
fluctuations from simulations or experimental observations. We apply
the framework to our all-atom molecular dynamics simulations of a
bacterial histidine kinase protein extensively studied in experiments.
For the isolated coiled-coil (CC) motif that connects sensor and effector
modules, our analysis reveals that signal propagation through the
CC is possible via shift, splay, and twist deformation modes, which
is confirmed by simulations of the entire protein. Based on mutation
experiments, we infer that the most relevant mode for the biological
function of the histidine kinase is the splay deformation. For the
β2-adrenergic receptor, a transmembrane protein involved
in the G-protein signaling pathway, we compare signal transmission
across its different structural domains involved in receptor activation.